\section{Rotorcraft Flight Dynamic Model}

\cite{abbeel_2009}

\begin{align}
\text{translational dynamics}\nonumber\\
\dot{u} &= v.r - w.q - g_u + C_u.[u]\\
\dot{v} &= w.p - u.r - g_v + C_v.[v]\\
\dot{w} &= u.q - v.p - g_w + C_w.[1; w; i_\text{col}.\Omega; \sqrt{u^2+v^2}]\\
\text{rotational dynamics}\nonumber\\
\dot{p} &= C_p.[1; p; i_\text{lat}.\Omega]\\
\dot{q} &= C_q.[1; q; i_\text{lon}.\Omega]\\
\dot{r} &= C_r.[1; r; i_\text{rud}.\Omega]\\
\text{and rotor dynamics}\nonumber\\
\dot{\Omega} &= C_\Omega.[1;\Omega; i_\text{col}; w; \sqrt{u^2+v^2}; i_\text{lat}^2+i_\text{lon}^2; i_\text{thr}]
\end{align}

